1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequentially Compactness

  1. Sep 16, 2008 #1
    Suppose that S is a nonempty set of real numbers that is not Sequentially compact. Prove that either (i) there is an unbounded seqeunce in S or (ii) there is a sequence in S that converges to a point x0 that is not in S.

    I am having trouble with this it not being sequentially compact is screwing me up, I don't know how to prove it.
     
  2. jcsd
  3. Sep 16, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Well, there are two ways you can proceed:
    (1) Suppose that S is bounded, and prove that there is a sequence in S that converges to something outside of S, or
    (2) suppose that every convergent sequence in S has a limit in S, and prove that S cannot be bounded.

    Have you tried either way? If so, what kind of problems did you run into?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Sequentially Compactness
  1. Compactness of a space (Replies: 3)

Loading...